Run-Length Constraint of Cyclic Reverse-Complement and Constant GC-Content DNA Codes

2020 ◽  
Vol E103.A (1) ◽  
pp. 325-333 ◽  
Author(s):  
Ramy TAKI ELDIN ◽  
Hajime MATSUI
Keyword(s):  
Gc Content ◽  
Run Length ◽  
Dna Codes ◽  
Length Constraint ◽  
Reverse Complement

scholarly journals Construction of Dual Cyclic Codes over {F}_{2}[u,v]/ for DNA Computation

2018 ◽  
Vol 68 (5) ◽  
pp. 467-472
Author(s):  
Manoj Kumar Singh ◽  
Abhay Kumar Singh ◽  
Narendra Kumar ◽  
Pooja Mishra ◽  
Indivar Gupta
Keyword(s):  
Cyclic Codes ◽  
Gc Content ◽  
Inner Product ◽  
Dual Codes ◽  
Dna Computation ◽  
Dna Codes ◽  
Reverse Complement

Here, we assume the construction of cyclic codes over ℜ={F}_{2}[u,v]/ < u^2, v^2 - v, uv - vu >. In particular, dual cyclic codes over ℜ= {F}_{2}[u]/ <u^2> with respect to Euclidean inner product are discussed. The cyclic dual codes over ℜ are studied with respect to DNA codes (reverse and reverse complement). Many interesting results are obtained. Some examples are also provided, which explain the main results. The GC-Content and DNA codes over ℜ are discussed. We summarise the article by giving a special DNA table.

scholarly journals Bounds for DNA Codes with Constant GC-Content

10.37236/1726 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Oliver D. King
Keyword(s):  
Lower Bounds ◽  
Hamming Distance ◽  
Gc Content ◽  
Maximum Size ◽  
Additional Constraint ◽  
Upper And Lower Bounds ◽  
Dna Codes ◽  
Minimum Hamming Distance ◽  
Reverse Complement

We derive theoretical upper and lower bounds on the maximum size of DNA codes of length $n$ with constant GC-content $w$ and minimum Hamming distance $d$, both with and without the additional constraint that the minimum Hamming distance between any codeword and the reverse-complement of any codeword be at least $d$. We also explicitly construct codes that are larger than the best previously-published codes for many choices of the parameters $n$, $d$ and $w$.

Codes With Run-Length and GC-Content Constraints for DNA-Based Data Storage

2018 ◽  
Vol 22 (10) ◽  
pp. 2004-2007 ◽  
Author(s):  
Wentu Song ◽  
Kui Cai ◽  
Mu Zhang ◽  
Chau Yuen
Keyword(s):  
Data Storage ◽  
Gc Content ◽  
Run Length

scholarly journals New DNA Codes from Cyclic Codes over Mixed Alphabets

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1977
Author(s):  
Hai Q. Dinh ◽  
Sachin Pathak ◽  
Ashish Kumar Upadhyay ◽  
Woraphon Yamaka
Keyword(s):  
Cyclic Codes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Block Length ◽  
Dna Codes ◽  
Reverse Complement ◽  
Gray Maps ◽  
Cyclic Dna Codes ◽  
One To One ◽  
Necessary And Sufficient

Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]⟨xα−1⟩×R[x]⟨xβ−1⟩×S[x]⟨xγ−1⟩. We discuss their generator polynomials as well as the structure of separable codes. Using the structure of separable codes, we study cyclic DNA codes. By using Gray maps ψ1 from R to F42 and ψ2 from S to F43, we give a one-to-one correspondence between DNA codons of the alphabets {A,T,G,C}2,{A,T,G,C}3 and the elements of R,S, respectively. Then we discuss necessary and sufficient conditions of cyclic codes over F4, R, S and F4RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.

scholarly journals On cyclic DNA codes over the rings Z4 + wZ4 and Z4 + wZ4 + vZ4 + wvZ4

BIOMATH ◽  
2017 ◽  
Vol 6 (2) ◽  
pp. 1712167 ◽  
Author(s):  
Abdullah Dertli ◽  
Yasemin Cengellenmis
Keyword(s):  
Cyclic Codes ◽  
Finite Ring ◽  
Finite Rings ◽  
Binary Images ◽  
Dna Codes ◽  
Reverse Complement ◽  
Skew Cyclic Codes ◽  
Cyclic Dna Codes

The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; w^2 = 2; v^2 =v; wv = vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are established, respectively. The cyclic codes of odd length over the finite ring R satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.

scholarly journals Improved Lower Bounds for Constant GC-Content DNA Codes

2008 ◽  
Vol 54 (1) ◽  
pp. 391-394 ◽  
Author(s):  
Yeow Meng Chee ◽  
San Ling
Keyword(s):  
Lower Bounds ◽  
Gc Content ◽  
Dna Codes

scholarly journals Zero Capacity Region of Multidimensional Run Length Constraints

10.37236/1465 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Hisashi Ito ◽  
Akiko Kato ◽  
Zsigmond Nagy ◽  
Kenneth Zeger
Keyword(s):  
Binary Sequence ◽  
Capacity Region ◽  
Run Length ◽  
One Dimensional ◽  
Coordinate Axis ◽  
Length Constraint ◽  
Zero Capacity ◽  
The One ◽  
Constrained Capacity

For integers $d$ and $k$ satisfying $0 \le d \le k$, a binary sequence is said to satisfy a one-dimensional $(d,k)$ run length constraint if there are never more than $k$ zeros in a row, and if between any two ones there are at least $d$ zeros. For $n\geq 1$, the $n$-dimensional $(d,k)$-constrained capacity is defined as $$C^{n}_{d,k} = \lim_{m_1,m_2,\ldots,m_n\rightarrow\infty} {{\log_2 N_{m_1,m_2,\ldots ,m_n}^{(n; d,k)}} \over {m_1 m_2\cdots m_n}} $$ where $N_{m_1,m_2,\ldots ,m_n}^{(n; d,k)}$ denotes the number of $m_1\times m_2\times\cdots\times m_n$ $n$-dimensional binary rectangular patterns that satisfy the one-dimensional $(d,k)$ run length constraint in the direction of every coordinate axis. It is proven for all $n\ge 2$, $d\ge1$, and $k>d$ that $C^{n}_{d,k}=0$ if and only if $k=d+1$. Also, it is proven for every $d\geq 0$ and $k\geq d$ that $\lim_{n\rightarrow\infty}C^{n}_{d,k}=0$ if and only if $k\le 2d$.

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